【摘要】 本文利用动力系统方法和奇行波方程理论研究广义Gilson-Pickering方程的动力学行为和行波解.利用软件画出了给定参数条件下系统的相图分支,得到了孤立波解、扭结波解和反扭结波解、不可数无穷多破缺波解、光滑周期波解和非光滑周期尖波解、尖孤子解的存在性.在β≠1,p=2时,对于广义Gilson-Pickering方程不同的参数条件下,给出了保证上述解存在的条件及参数表示.更多还原

【Abstract】 In this paper,we study the dynamical behavior and traveling wave solutions using the method of dynamical systems and theory of singular traveling wave equations for generalized GilsonPickering equations.We draw the phase portraits bifurcations of the system with given parameters using maple,and the existence of solitary wave solutions,kink wave solutions and anti-kink wave solutions,uncountablely infinite many breaking wave solutions,smooth periodic wave solutions,non-smooth periodic cusp wave solutions and peakon solutions is obtained.When the conditions that β≠1,p=2,we give the existing conditions ensureing above solutions and parametric representation of the solutions for various sufficient conditions of the generalized Gilson-Pickering equation.更多还原